Coppell has been in charge of Reading for five years, taking them up to the top flight two seasons ago and to a magnificent eighth-place finish last year.
Despite that achievement, Madejski said relegation had not come as a huge surprise 12 months on, and called for a collective share of responsibility for the downturn in results.
"Things haven't been looking rosy for a while. It's not a very nice thing to happen, but you have to be philosophical about it," he said.
"So as far as I'm concerned for the sake of the fans we have to get things right and move on. I think that everyone's culpable, including myself, certainly the players are."
Coppell has indicated he will take his time over a decision on his future.
"I have got to look at things. I have a huge affection for this club and I want to do what I think is right for this club," he said.